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kifflom [539]
3 years ago
6

In circle A shown below, Segment BD is a diameter and the measure of Arc CB is 48°:

Mathematics
2 answers:
marshall27 [118]3 years ago
8 0

Answer:

66°


Step-by-step explanation:

<em>See attached picture.</em>

<em>When an angle intercepts an arc, </em><em>ARC AC</em><em>, and forms in the </em><em>center [central angle]</em><em>, the angle has </em><em>SAME</em><em> measure as the ARC AC </em><em>[denoted by x]</em><em>. When the angle formed is on the opposite side, it has a measure </em><em>HALF</em><em> of that ARC AC </em><em>[denoted 0.5x ]</em>


If you look at the problem given, ∠DBC is intercepted by ARC DC and falls in the opposite side of the circle, NOT in the CENTER. <em>Hence </em><em>∠DBC</em><em> has a measure that is </em><em>HALF of ARC DC</em><em>.</em>

<em>There are </em><em>360 degrees in a circle.</em><em> </em><em>ARC DB</em><em> has 2 endpoints that are the diameter of the circle, so </em><em>ARC DB</em><em> has a measure of </em><em>180 degrees</em><em>. </em>Also,


ARC DB = ARC DC + ARC CB

ARC DB = ARC DC + 48

180 = ARC DC + 48

ARC DC = 180 - 48 = 132


Since, ∠DBC = 0.5 * ARC DC, we have:

∠DBC = 0.5 * (132)

∠DBC = 66

Our answer is the second choice of 66°.

SCORPION-xisa [38]3 years ago
4 0
Hello,

<span>Arc CD=180°-48°=132°
</span>
<span>the measure of ∠DBC=132°/2 =66°

</span>Answer B

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